Riemann–Roch Theorem

(Theory)

Logo of Riemann–Roch theorem
skills
Theory since 1865
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What is Riemann–Roch theorem?

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings. Initially proved as Riemann's inequality by , the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch . It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.

Technology Types

bernhard riemanngeometry of divisorknow-howmathematical theoremmethodpropositionstatementtheoremtheorems in algebratheorems in algebraic geometrytheorems in complex analysistheorems in geometrytheorytopological methods of algebraic geometry

Synonyms

Riemann RochRiemann Roch for curvesRiemann Roch theoremRiemann-RochRiemann-Roch formulaRiemann-Roch problemRiemann-Roch TheoremRiemann-Roch theorem for algebraic curvesRiemann-Roch theorem for Riemann surfacesRiemann–Roch formulaRiemann–Roch theorem for algebraic curvesRiemann–Roch theorem for Riemann surfacesRiemann's inequality

Translations

Satz von Riemann-Roch (de)Stelling van Riemann-Roch (nl)Théorème de Riemann-Roch (fr)Теорема Римана — Роха (ru)Теорема Рімана — Роха (uk)리만-로흐 정리 (ko)リーマン・ロッホの定理 (ja)黎曼-罗赫定理 (zh)

Tech Info


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